If a new survey from the Council of Public Relations Firms is to be believed, public relations professionals believe that Ford is winning the public relations war against its former supplier Bridgestone-Firestone—but the automaker’s biggest mistake may be the assumption that one company must lose the war in order for the other to win.

The survey, which tallied responses from 87 of the 130 members of the Council, found two-thirds majorities supporting Ford’s decision to recall 13 million Firestone tires and opposing Firestone’s pre-emptive decision to sever its relationship with the automaker. But an even greater majority (85 percent) agreed that “if Ford and Firestone had worked together, instead of publicly attacking each other, their 95-year-old business relationship could have been be saved and the damage done to their credibility and to consumer confidence in both companies been avoided.”

That judgment comes at a time when both companies are stepping up their attacks. On May 22, after it became apparent that Ford was about to initiative a recall of 13 million Firestone tires, Firestone severed its relationship with the automaker. A week later, the Japanese company asked the National Highway Traffic Safety Administration to look into overall stability issues with the Ford Explorer. And on Friday, Ford made the case that Firestone tires fail faster than other brands.

It’s always difficult to judge a crisis from the outside looking in, since internal communications executives almost always have access to data not apparent to external audiences. But as tensions between the two parties in the Ford-Firestone crisis have escalated, it seems to many as though both companies view the crisis as a zero-sum game.

That may be true in the litigation arena, but it is clearly false in the public relations realm, where every attack that Ford launches against the tire maker inflicts substantial collateral damage on the car company’s own reputation, and vice versa. That has led many observers to conclude that Ford’s recent strategy is being driven more by legal concerns than by the need to protect the company’s brand.

Having said that, most public relations experts believe that if anyone is winning the PR war, Ford is. In addition to the Council survey, a recent poll conducted at our website, http://www.provokemedia.com/, found that while 41 percent thought both parties were suffering as a result of the high visibility sniping, 38 percent believed Ford was winning, compared to just 21 percent who felt Bridgestone-Firestone had the upper hand.

Since the data do not appear to support the idea that Ford is less culpable than Firestone, the fact that Ford is so clearly ahead of its supplier in public relations terms allows us to draw two lessons from the crisis to date.

The first is that reputation—and attendant goodwill—matters. Before the crisis struck, Ford had a much higher profile than Firestone, and enjoyed a good reputation among all its stakeholders. The company had invested heavily in its brand, and enjoyed the trust of its customers and the public at large. In contrast, Bridgestone-Firestone had invested very little in corporate reputation—its public relations team spent most of its time promoting the company’s auto racing sponsorships.

(Bridgestone-Firestone did not even have an office in Washington, and while it has scrambled to establish a presence there, the fact that it has few solid relationships in the nation’s capital is likely to be a major hindrance as congressional hearings get under way this week.)

The second lesson is that the tone of a company’s response can be more important than cold hard data. In the early days of the crisis, Ford came across as more concerned about consumer safety, more responsive, and more communicative—a perception that was reinforced by the speedy way it resolved many of the legal claims against the company.

It has long been apparent that consumers judge a company more on the way it responds to a crisis than on the occurrence of the crisis itself. That rule appears to be more true in this case than in most. As Nikko Salomon Smith Barney analyst Tsunemi Tachibana pointed out after Bridgestone-Firestone ended its 95-year relationship with Ford, “Bridgetsone believes its data hold up. But tire buyers likely won’t care. For the users, they don’t know the exact quality of technical issues.” Unable to make their judgments based on exhaustive study of the evidence, consumers are likely to go with their gut instincts about who can be trusted and who can’t.

But Ford’s most important challenge is not to emerge from the crisis with a higher level of public trust than Firestone, but rather to protect its reputation. The two are not synonymous, and there are signs that Ford’s reputation is taking a heavy battering, with this week’s Business Week questioning quality and morale inside the company.

From an outsider’s perspective, it appears that there is plenty of blame to go around. Firestone tires on other vehicles appear to pose no significant risk; Explorers without Firestone tires appear to be as safe as other SUVs. There appear to be problems with the tires—particularly with a single batch from a plant in Deactur—but there also appear to be issues with the Explorer, including the instructions that Ford gave to consumers regarding tire pressure.

Regardless of how regulators—and the courts—adjudicate this matter, the public’s confidence in both companies has been shaken.